Hi,

You can create a new invoice on button click. For that search the service product and store it in a variable using search method.Then create corresponding invoice by adding that product.
For creating invoice you will have to pass values to the fields which are required for an invoice.

Example

invoice = self.env['account.move'].create({
   'move_type': 'out_invoice',
   'invoice_date': fields.Date.today(),
   'partner_id': self.customer_id.id,
   'l10n_in_gst_treatment': self.customer_id.l10n_in_gst_treatment,
   'currency_id': self.currency_id.id,
   'invoice_line_ids': [(0, 0, {
       'product_id': self.product_id })],
})

Regards